Although the idea of a knight or lord freely raping, kidnapping, seducing, murdering in the heat of passion a peasant girl under his power has been a source of lurid fascination with the Middle Ages since, well, since the Middle Ages themselves, it was absolutely not a systematic practice for a whole host of reasons: religious, legal, moral, political. We can see especially in accounts of warfare that sexual violence was indeed a deep concern for medieval women themselves, and certainly it was a preoccupation for medieval clerics frequently more concerned with women's chastity than women themselves were--but no, women were not worrying about the duke sweeping them off to the castle for a fortnight or a lifetime.

First, from a religious-legal and hence moral perspective, both Christian canon law (which regulated sex and marriage) and Islamic law prohibited either rape or additional marriage. Canon law barred sex outside marriage as well as multiple spouses, and was very very restrictive on opportunities for divorce. There are cases in early medieval Italy of lords practicing bigamy or keeping official concubines, and surely there were plenty of unofficial ones elsewhere and in later years, but neither rape or kidnapping someone else's wife were approved practices. Islamic law limits sex to either marriage or a master with his own female slave, in which case she accrues special protection. (And the law limits this practice to slaves the man, specifically, owns--even his wife's personal slaves are off limits). While men can have multiple wives, the reverse is not true. So Islamic lords in al-Andalus are also not plucking random peasant wives for themselves. (Muslims cannot be made slaves by other Muslims, legally, so that's not a loophole).

Second, the question of marriage. No, a lord is not going to marry a random peasant. Marriage among the medieval nobility was a political institution first and foremost, however the Church tried to promote it (and make no mistake, the Church's interest in marriage was because it was such a political force--ranking medieval clerics were all nobles themselves, and they wanted a say in who got married, reproduced, and had either money or children to donate to the Church). Generally, parents either had potential spouses for their children picked out long in advance--the Church set a lower bound on betrothal age to 7, but it was basically ignored--or had to conduct extensive diplomatic campaigns to find a good political match...to whom the child was not already related.

Nevertheless, the idea that a lord could and would seduce/rape a lowly born woman was a mainstay of medieval literary imagination, as well as our picture of the Middle Ages today. The medieval lyric genre of pastourelles, popularized by the troubadour poets in 12th century France but with enduring popularity throughout western Europe, offered a counterpart to the (ideally) unconsummated courtly love tradition of noble lovers who (ideally) cannot physically demonstrate their love.

In pastourelles, a knight or other aristocratic character traveling across the countryside happens upon a country girl, prototypically a shepherdess. Verbal sparring ensues. Sometimes she proves the superior wit and he passes on his way; sometimes she consents and they have sex; sometimes she refuses and he rapes her. Just as courtly romances teased the lure of the forbidden--the king's queen, the other knight's wife that you mustn't dare touch--pastourelles played upon the same thrill of the unfulfilled-by-its-audience forbidden.

Today, we are more familiar with the jus primae noctis or the more picturesque French term droit de cuissage, "right to the thigh", above all from that most accurate of medieval documentaries Braveheart. In this schema, medieval lords had the perfectly legal and ecclesiastically-approved right to have sex with any serf woman on her wedding night (the "first night" or prima nox). As noted above, this was in fact not legal or moral. So how did we get here?

There are some 14th century sources from the Low Countries to the effect that if a male serf chooses to marry a woman from another lord's dominion, and consequently bring her to live with him, his lord must compensate the other lord for the loss of her labor. This makes reasonable sense as an actual medieval practice.

But by 1500, this has become canon lawyer Nicolas Boyer's exquisite phrase, "the lords of Gascony had the right to place a bare leg across the newlyweds’ bed." In other 16th century references, the "right" is claimed by lords in different parts of France, pertains to male or female serfs variously, and--tellingly--is noted as "obscene" with the specific mention that such a practice has now, in a more civilized age, been replaced with lavish feasting.

We still turn to this myth today, with works from Braveheart to (sadly, because it's an amazing book) Pillars of the Earth using droit de cuissage as a way to denote the shocking brutality and evilness of certain characters--and by extension, the era that permits their actions. But in that way, anchoring the practice of this form of systematized violence against women so firmly in the past has allowed us us--from the age that saw themselves as the renaissance of civilization, to today--to step back and say, We are not like that. We are better; we are civilized.

The rights of serfs, tenants and in some cases self-owning peasants varied with place, time and wether we talk theoretical or practical rights.

In the end, laws were usually much more fuzzy than nowadays, and the ability of the offended party to bring the offender to justice played a large part in wether or not they could or would do something.

For example, Bo Jonsson (Grip), Lord Chancellor of Sweden and the richest man in the country brutally murdered fellow nobleman Karl Nilsson (Färla) in church 1382, suspecting Karl Nilsson (Färla) of having an affair with his wife, the alledgedly beautiful Margareta Dume. Bo Jonnson (Grip), who controlled about 1/3 of the arable land in the country at the time (through inheritance and pawned off land and its tax income from the crown as the security for various loans) faced no reprecussions for his deed.

That said, even the lowest serfs (those in Eastern Europe) had the right to have a family and to private ownership. The catholic or orthodox church, both very powerful institutions would not appreciate bigamism (ie marrying an already married woman). The church viewed marriage as a holy business of the church, and nobility trying to interfer with it could face serious problems, including banishment from the church.

In some countries, the serfs had the right to petition higher authority - either the King himself or a higher nobleman which their nobleman was a vassal to. Their ability to do so would often depend on their resources. Again, pissing off people with resourced, contacts and determination, especially if you had enemies that would sieze on the opportunity against you when people you have treated cruelly petition your lord or the king.

The Swedish peasants petitioned the Danish King (then King also over Sweden) numerous times about their tax collectors not respecting their rights, attempting to pressure more money than owed to the crown and treating the peasants roughly (beating them up, plundering farmsteads and so on). The lack of a response from the King led to the Engelbrekt rising in 1443 which saw a majority of tax collectors killed, their castles or forts burned and the King ousted.

In many countries, serfs had a week per year when they could and would switch landlords. A nobleman who treated his serfs exceedingly badly would see a lot of them move, and perhaps face a problem with labour - too few hands to tend the fields and animals he owns and thus reduced income.

In many countries, the nobility earned the right to "hand and neck" on their estates and manors, meaning they could be the prosecutor, judge and hangman in one.

With such power, coercion comes pretty easy, and it was not uncommon for noblemen to have a series of bastards. That said, money and power, good manners and speech as well as being able to afford to be charming and well-dressed could very well lead to many voluntary relationships.

Some took good care of their bastards and their mothers, others sent them away to fend for themselves.

Marrying was serious business though, and a nobleman who took a lowborn as a wife could face the disdain of his peers, forfeited any potential inheritance and dowry the family of a noble woman could provide, not even speaking of a potential alliance through marriage.

As per your original question, yes he could. He could accuse her husband of a crime and execute him (if he had the right to "hand and neck"), make her his ward and then marry her if he had a compliant priest or other church official and then force her to live as his wife. If he can block the families of the killed husband and now Lady from petitionig the church, King or higher nobleman, are powerful enough to prevent any kind of rebellion or taking to the forest in a low-level guerilla war (akin to the mythical Robin Hood) and make sure the disdain of his peers of him marrying below his status does not affect him, he can.

If he cannot do all these things, he willprobably suffer some consequences. What they will be will vary depending on the country, the time, the situation, the relative power of other nobility, the peasants, the church and other authorities.

/r/Jonjonmackey82 do you mind me asking why you thought this was a thing in the first place? I've never heard of this idea